Unit 3 Fractional Division
Countdown to the first class
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and their ability to judge and reason.
Knowledge goal:
Can clearly know the concept of reciprocal, can find the reciprocal of a number.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, and feel that mathematics comes from life.
Teaching emphasis: Can find the reciprocal of a number.
Teaching strategies:
On the basis of communication and cooperation between groups, the concept of reciprocal is obtained, and the reciprocal of a number can be found.
Teaching preparation: projector.
Teaching process:
First, introduce new lessons.
Introducing the new lesson with the formula of fractional multiplication.
Second, learn the concept of equivalence.
1. Show the following formula with a projector.
× = 2× = × = × 10=
× = 7× = × = ×5=
2. Ask the students to calculate the result of the above formula first and tell the answer.
(Middle and lower reaches students answer)
3. Communicate the rules of the formula in the group, and then communicate with the whole class.
4. Teacher's summary: If the product of two numbers is 1, then we call one of them the reciprocal of the other.
5. Say that one number is the reciprocal of another number, and other students will judge and comment.
Third, consolidate the goal.
Show the test questions, students do them independently, correct them at the same table after they finish, and finally answer them by name.
Fourth, teachers ask questions and students exchange and discuss.
Is there a reciprocal of 0? Communicate your ideas with your classmates.
Fifth, practice consolidation.
Practice the topic, do it independently, and correct it in the whole class.
Sixth, class summary and teacher evaluation.
Blackboard design:
reciprocal
a× = (a≠0)
Teaching reflection:
Fractional Division in the Second Classroom (1)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and their ability to judge and reason.
Knowledge goal:
Experience the calculation method of dividing score by integer, summarize the calculation rules on the basis of discussion and exchange, and calculate correctly.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the fun of operation.
Teaching emphasis: Can find the reciprocal of a number.
Teaching strategies:
On the basis of communication and cooperation among groups, a conclusion is drawn through calculation.
Teaching preparation: a rectangular piece of paper.
Teaching process:
First, introduce new lessons.
Students, we have learned fractional multiplication before. At first, we learned the fractional multiplication of integers. Can you divide fractions? Today we are going to learn how to divide fractions into integers. Do you like it?
Second, learn new lessons.
1, learning ÷2
Ask the students to take out a rectangular piece of paper and divide it into two parts equally. First, divide the four parts into two parts, smear them and name the results.
2, learning ÷3
Students are required to divide a piece of paper into 3 points on average. How to divide it?
Answer by name, and other students will add comments.
After dividing them, draw them with a pen and see how much each one costs.
3. Learn the meaning of fractional division.
Question, what do you think of the first two formulas? Why use division? Say it.
Communicate in groups and finally communicate with the whole class. The teacher summed it up. Evaluation.
4. Learn the calculation rules.
Show the following questions
1÷4= 10÷5= 7÷3=
1× = 10÷ = 7× =
After the students calculate independently, ask what you found. Can you tell the calculation rules of division?
Group communication, and finally the teacher summed up:
Dividing by an integer (except zero) is equal to multiplying the reciprocal of this integer.
Third, the class summary:
Ask questions and communicate. What did we mainly learn in this class? Students answer and teachers evaluate.
Blackboard design:
Fraction divided by integer
÷c= × (a、c≠0)
Teaching reflection:
Division of the Third Fraction (2)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and their ability to judge and reason. Draw a conclusion through analysis.
Knowledge goal:
Experience the calculation method of integer divided by fraction, summarize the calculation law and calculate correctly on the basis of discussion and communication.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the fun of operation.
Teaching emphasis: the derivation process of the calculation rules of integer divided by fraction.
Teaching strategies:
On the basis of communication and cooperation among groups, a conclusion is drawn through calculation.
Teaching preparation: projector
Teaching process:
First, introduce new lessons.
In the last lesson, we learned the calculation method of dividing a fraction by an integer. Do you remember? Will the teacher test you? See the problem.
÷5= ÷4= ÷7=
Name the calculation method and results, and evaluate them. Then in this lesson, we will continue to learn the calculation method of integer divided by fraction. All right. (good)
Second, learn to divide integers by fractions.
Display the title of the textbook with a projector
1. There are four identical cakes, each of which is a replica. How many shares can it be divided into? Name answer: 4÷2=? And tell the basis of the formula.
There are four identical cakes, each of which is a piece. How many pieces can it be divided into?
Answer by name: 4÷ 1=? And tell the basis of the formula.
There are four identical cakes, two for each. Let the students draw a picture, color it, and then discuss it in groups. Finally, the whole class communicates and answers by name.
Teacher's summary: From the picture, the result is 8,4 ÷ = 8, which is ok.
4×2=8.
There are four identical cakes, one for each. How many can they be divided into? Every piece of paper is a copy. How many shares can it be divided into? Solve these two problems in the group, then communicate with the whole class and the teacher evaluates them.
Third, the teaching of calculation rules.
Show me the title.
4÷ ( )4×2 4÷ ( )4×3
4÷ ( )4×4 2÷ ( )2×2
2÷ ( )2×3 2÷ ( )2×
Let the students calculate and exchange the results first. Then ask questions. What can you find by looking at the formula and the result?
Classroom communication, teacher summary:
Dividing by a number (except zero) is equal to multiplying the reciprocal of this number.
Fourth, consolidate the goal.
1, draw a picture in the textbook.
First, instruct the students to draw a line segment diagram in the exercise book, and then list the formulas and calculate the results with the line segment diagram. Judge at the same table
2. Try the topic.
Calculate independently and answer by name.
Fifth, class summary.
Blackboard design:
Integer divided by fraction
a \ = a×(b、c≠0)
Teaching reflection:
The fourth lesson fractional division practice class (2)
Teaching objectives:
Ability goal: to cultivate students' ability to use their hands, brains and calculations.
Knowledge goal:
Experience the calculation method of integer divided by fraction, and can calculate it correctly.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: the calculation method of integer divided by fraction.
Teaching strategies:
On the basis of communication and cooperation among groups, improve the computing ability and speed.
Teaching preparation: small blackboard
Teaching process:
First, introduce new lessons.
In the last lesson, we learned the calculation method of dividing an integer by a fraction. Do you remember? Will the teacher test you? See the problem.
6÷ = ÷ = ÷ = ÷ =
2÷ = ÷ = ÷ = ÷ =
Ask questions, review the whole class and introduce new lessons. And evaluate it.
Second, use the small blackboard to show the following questions.
3x= x= 10 x=25 x=
Ask the students the law of solving equations and tell the solution to the first small problem.
Other topics are written independently and revised by the whole class.
Third, the third question in the textbook
Say the meaning of the topic, then answer, and the class decides.
Fourth, the fourth question.
1, independent calculation first, class correction.
2. What rules have been found in the communication between groups?
3. Communicate with the whole class.
4. The teacher summed it up.
Blackboard design:
Integer divided by fraction
The quotient divide by that true fraction is greater than an integer.
The quotient of an integer divided by a fraction and then divided by 1 is an integer.
The quotient divided by the false fraction is less than an integer.
Teaching reflection:
Lesson 5 Fractional Division (3)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and solve practical problems.
Knowledge goal:
Improving the calculation speed and accuracy of fractional division can correctly calculate and solve practical problems.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: solving practical problems.
Teaching strategy: on the basis of communication and cooperation among groups, improve the computing ability and speed.
Teaching preparation: small blackboard
Teaching process:
First, introduce new lessons.
Students, our mathematics comes from the experience and crystallization of life, and also serves life. So what problem can our fractional division solve? In this lesson, we will learn the application of fractional division. Theme on the blackboard: Fractional division (3)
Second, implement the goal.
1, display topic:
There are six children skipping rope, which is the total number of people participating in the activities on the playground. How many people are there on the playground?
2. Call the students to read the questions and say who is the unit of "1" in the questions? Do you know that?/You know what?
3. Let students try to do it first.
4. Exchange practice. (Method of introducing equations according to students' questions)
5. The teacher guides students to solve problems with equations. For students who answer in other ways, just give them reasonable praise.
6. Infiltrate arithmetic to solve this problem.
7. Teacher's summary: As long as the quantity of the unit "1" is unknown, there are two ways to solve the problem, one is equation; One is arithmetic.
Third, consolidate the goal.
1, try the first question.
Ask the students to read the questions and answer them independently. According to the situation of students solving problems, give guidance to underachievers.
Guide students to distinguish the difference between two problems and know the difference between multiplication and division.
2. Try the second question.
Independent answer, class correction.
Fourth, class summary, teacher evaluation and students' self-evaluation.
Blackboard design:
Fractional division (3)
Solution: suppose there are x people participating in the activity on the playground.
X× =6
x÷= 6
X=6 times
X=27
Teaching reflection:
Lesson 6 Practice of Fractional Division (3)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and solve practical problems.
Knowledge goal:
Improving the calculation speed and accuracy of fractional division can correctly calculate and solve practical problems.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: solving practical problems.
Teaching strategies:
On the basis of communication and cooperation among groups, improve the computing ability and speed.
Teaching preparation: small blackboard
Teaching process:
First, introduce new lessons.
Students, last class we learned the application of fractional division. Do you remember? We will continue to study this course.
Second, implement the goal.
1, practice the first question
It means that two students rehearse 1 and two small questions, and the other students do exercises. After finishing, the whole class will correct it. The key point is to let the students check the mistakes in the rehearsal and find out the reasons for them.
Then do other topics independently. Deskmate revision.
2. The second question, let the students compare the discount topics they have done before and point out the similarities and differences.
Do it independently and tell the process, result and idea.
3. the third question reads the topic by name and tells the meaning of the topic. Who is the amount of the unit "1" of sum? List formulas. Tell the basis of the formula. Then do it independently.
4, the fourth question, because this question is difficult, it is recommended to communicate in the group first, and then communicate with the whole class. The same thoughts and opinions.
Third, class summary and evaluation.
Blackboard design:
Fractional Division Practice Class (3)
1, find out the number of units "1"
2. Determine what method or equation to use.
Teaching reflection:
Lesson 7 Exercise 3( 1)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and solve practical problems.
Knowledge goal:
Improving the calculation speed and accuracy of fractional division can correctly calculate and solve practical problems.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: solving practical problems.
Teaching strategies:
On the basis of communication and cooperation among groups, improve the computing ability and speed.
Teaching preparation: small blackboard
Teaching process:
First, introduce new lessons.
Students, we have learned the application of fractional division before, so let's practice it in this class, shall we?
Second, the implementation objectives
1, first question.
Say the concept of reciprocal, and then say the reciprocal of these books. Other students commented.
2. The second question.
First, let the students recall the calculation rules of fractional multiplication and fractional out-of-place, and then calculate independently, and the whole class will correct them together, with the emphasis on mistakes.
3. The third question.
By playing games, divide the students into two groups and have a game to see which group is doing it right and fast. The teacher counts the time according to the speed and accuracy of the students.
4. The fourth question.
Read the questions, point out who is the unit of "1" and explain the basis of the calculation method.
List the formulas and tell the results.
Other students judge and teachers evaluate.
5. The fifth question.
The method is the same as the fourth question.
Third, the teacher summed it up.
Blackboard design:
Exercise 3
Countdown to 9. Countdown seconds
Teaching reflection:
Lesson 8 Exercise 3 (2)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and solve practical problems.
Knowledge goal:
Improving the calculation speed and accuracy of fractional division can correctly calculate and solve practical problems.
Emotional goals:
Cultivate students' willingness to communicate and cooperate in groups, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: the calculation speed and correct rate of fractional division.
Teaching strategies:
On the basis of communication and cooperation among groups, improve the computing ability and speed.
Teaching preparation: small blackboard
Teaching process:
First, introduce new lessons.
Show the following formula for students to calculate.
÷ = ÷ = ÷4= ÷2=
Name the calculation results, review the whole class and introduce new lessons. This is the calculation of division, so we will review the application of deviation in this class.
Second, the application of division.
1, question 6.
Let the students read the questions and point out the conditions and problems in the questions. Who is this unit "1"? Students make their own calculations and finally the whole class corrects them.
2. The seventh question.
Ask the students what mathematical information this picture tells us. Can you list the formulas? Pointed column, students calculate independently, and correct at the same table. Comment.
3. The eighth question.
The method is the same as above, but students are required to calculate the problem in two ways. Teachers patrol, mainly to coach underachievers.
4. Question 9.
After showing the questions, ask the students to explain what 60% discount means, then work out the formula independently and correct it together.
5. Question 10
Independent homework, teacher patrol, problem-oriented, key counseling.
Third, class summary and teacher evaluation.
Blackboard design:
The eighth question
Arithmetic: 7.9 points =
Equation: Let the speed of the spacecraft be about x kilometers per second.
x=7.9
Teaching reflection:
Organize and review Lesson 9 (1)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and organize knowledge systematically.
Knowledge goal:
Improving the calculation speed of dividing an integer by a fraction can correctly calculate and solve practical problems.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: solving practical problems.
Teaching strategies:
On the basis of communication and cooperation among groups, improve the computing ability and speed.
Teaching preparation: small blackboard
Teaching process:
First, introduce new lessons.
Students, we have learned a lot before. Can you organize it systematically? All right. Next, you can sort out what you have learned before.
Second, the implementation objectives
1. The students simply sort out what they have learned and communicate in groups. The teacher patrolled and gave guidance.
According to your knowledge, can you tell me something? Call the students to answer the main content of the previous study, and the teacher summarizes it.
3. What problems did you find in finishing? Please bring them up and let's study together.
Students ask each other questions and answer each other. If there are problems that cannot be solved, deposit them in the problem bank.
Third, consolidate the goal.
1, practice the first question.
Students make their own calculations, and the teacher visits the key counseling and answers by name.
2. The second question.
Ask the students to say the conditions and questions of the topic and calculate them independently. After the calculation, tell the basis of the formula and comment on each other.
3. The third question.
After showing the topic, the topic tells us the length, width and height. Can we calculate her surface area? 10 set meal? What is the meaning of at least in the title? Students calculate independently. Review the whole class.
4. The fourth question.
Students work independently and the whole class corrects them. Teachers patrol and guide underachievers.
5. Question 6
The title tells us two groups of seats. How can we get all the seats in the cinema? Answer by name, then calculate independently, and the whole class will comment.
Fourth, the teacher summed it up.
Blackboard design:
Third question
Length: 7 cm
Width: 5cm surface area × 10
Height: 3 cm
Teaching reflection:
Summary and review of the tenth lesson (1)
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and organize knowledge systematically.
Knowledge goal:
Improve the calculation speed of integer divided by fraction, and can calculate correctly and solve practical problems.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: solving practical problems.
Teaching strategy: on the basis of communication and cooperation among groups, improve the computing ability and speed.
Teaching preparation: small blackboard
Teaching process:
First, the introduction of new courses.
Use the knowledge introduced in the last lesson.
Second, continue to study and practice topics in an exercise.
1, question 6.
Students do it independently. Tell the difference between the conditions and the questions. Is it related to the different methods of solving problems? Ask the students to compare the differences between multiplication and division.
2. The seventh question.
Show the questions, read the questions by name, and say what is the unit of each score "1"? Then do it independently and the whole class will revise it together.
3. The eighth question.
Read the title by name and tell the meaning of the title. Is there any change in the height in the topic?
Do it independently and modify it at the same table.
4. Question 9.
Guide the students to read the data in the table clearly, work independently, and correct it in the whole class.
Third, the teacher summed up the evaluation.
Blackboard design:
Question 9
168× =
168× =
168× =
168× =
Teaching reflection:
Lesson 1 1 Math and Life: Painting the Wall
Teaching objectives:
Ability goal:
Cultivate students' ability to use their hands and brains and solve practical problems.
Knowledge goal:
Calculate and solve practical problems on the basis of students' hands-on, know which parts of the wall should be painted and which parts should not be painted, and calculate the area of the painted wall.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: solving practical problems.
Teaching strategies:
On the basis of communication and cooperation among groups, improve the computing ability and speed and solve practical problems.
Teaching preparation: projector
Teaching process:
First, the introduction of new courses.
student We have studied the calculation of the surface areas of cuboids and cubes. What are the applications in real life? We will study in this class.
Write on the blackboard: paint the wall
Second, the measurement calculation
1, calculation of drawing blackboard
Take the group as a unit: measure the length and width of the two blackboards in front and back of the classroom respectively. After the measurement, calculate the area to be painted. After the calculation, the whole class corrects and the teacher evaluates.
2. Calculation of left and right wall painting area
What data need to be measured when painting the front and rear walls and removing the area of doors and windows? Answer by name, and then measure and calculate in groups.
Step 3 buy paint
① Know the size and price of the package.
(2) According to the first question and condition, students independently calculate the pigments used in the first painting.
(3) Second question, the pigment used for the second time is the pigment obtained from the first and second painting.
Third, consolidate the goal.
Practice the questions in the exercises. Students work in groups, calculate, communicate with the whole class, and evaluate by teachers.
Fourth, the teacher summary
Ask the students to tell the content of this lesson.
Blackboard design:
whitewash a wall
Measure-Calculate-Buy
Teaching reflection:
Lesson 12 Folding
Teaching objectives:
Ability goal: through folding, cultivate students' ability to use their hands and brains and solve practical problems.
Knowledge goal: calculate and solve practical problems on the basis of students' hands-on.
Emotional goals:
Cultivate students' sentiment of being willing to communicate and cooperate, like mathematics, feel that mathematics comes from life and experience the joy of success.
Teaching emphasis: solving practical problems.
Teaching strategy: On the basis of group cooperation, we can achieve the purpose of this lesson through games.
Teaching preparation: rectangular pieces of paper
Teaching process:
First, the introduction of new courses.
The students all like handicraft classes. Are we going to have a handicraft class today? Introducing a new lesson "Folding"
Second, the implementation objectives
1, show the graphics of the textbook and let the students tell all kinds of data.
2. Think about what the figure is after folding according to the dotted line, and express your thoughts.
3. Fold your own papers according to the textbook, and the teacher will evaluate them according to the students' performance.
4. Ask a new question: If you open a skylight and a door, where is it? Communicate with each other in the group and then communicate with the whole class.
5. Mark the position of the skylight and the child on the map again.
Third, consolidate the goal.
1. Do-it-yourself problem: Let the students cut out the picture 1 in Appendix 3, fold it into a closed three-dimensional figure according to the dotted line, and draw the skylight and the door. Switch the positions of the skylight and the door at the same table and tell your reasons.
Step 2 give it a try
Calculate its actual length and area first, then do it, do it independently, and correct it in the whole class.
3. In practice, 1 and 2 questions are folded independently, and excellent works are selected from the group for class communication and teacher evaluation.
4. Practice the third question.
Solve problems in groups, and finally communicate with the whole class.
4. Homework after class: Question 4
Fifth, class summary.
Blackboard design:
fold
Measure-Calculate-Dashed Line-Fold
Teaching reflection: